Numerical methods for stochastic differential equations based on Gaussian mixture

We develop in this work a numerical method for stochastic differential equations (SDEs) with weak second order accuracy based on Gaussian mixture. Unlike the conventional higher schemes SDEs It\^o-Taylor expansion and iterated It\^o integrals, proposed scheme approximates probability measure $\mu(X^{n+1}|X^n=x_n)$ by mixture of Gaussians. The solution at next time step $X^{n+1}$ is then drawn from complexity linear dimension $d$. This provides new general strategy to construct efficient high SDEs.